Highly aggressive forms of tax avoidance should be regarded in a similar way to illegal tax evasion, David Cameron has said as he called on businesses to pay their fare share of tax.

In his first public engagement on his trip to India, the prime minister said tax avoiders should face a moral obligation to pay up because of the difficulties in cracking down on complex tax schemes.

Cameron was speaking at the Mumbai headquarters of Unilever at the start of a three-day visit to India that is designed to underpin trade links with the booming subcontinent. India is on course to be the world's third largest economy by 2030.

In his first announcement the prime minister responded to criticisms from business leaders in India and Britain, who have complained of restrictive visa requirements, by saying that Indian investors would be able to apply for a British visa in a day.

Cameron also announced that Britain is to help build an economic corridor between Mumbai, India's traditional business capital, and the hi-tech centre of Bangalore. Britain is to provide £1m towards a feasibility study if the Indians provide match funding.

The prime minister is taking the largest trade delegation ever to accompany a British prime minister on his visit to India. His chartered Virgin plane had 164 passengers including captains of industry, leaders of small to medium enterprises (SMEs), a host of university vice-chancellors and nine parliamentarians with Indian heritage.

In his 30-minute question and answer session at the Indian headquarters of Unilever the prime minister touched on India and beyond as he:

• Advised India to start big public transport infrastructure projects as quickly as possible to avoid delays, though he declined to mention the delays in fulfilling his wish for greater airport capacity in London.

* Provided fuel for critics of "Chillaxing Dave" by speaking of the importance of delegating work. He said it was important to "have a team you can work with and get things done for you".

• Broke with Margaret Thatcher, who famously survived in Downing Street on three hours sleep a night, by saying he tries to get a good night's sleep. "If you are exhausted and if you are fried mentally you will be a hopeless prime minister."

On tax the prime minister said the time had come to challenge the distinction between tax evasion, which is illegal, and tax avoidance, which is legal. Cameron said businesses have no excuse to avoid paying their fair share of tax in Britain after his government cut corporation tax to a competitive 21%.

The prime minister said: "The lesson for business should be if we are cutting this rate of tax down to a good low level you should be paying that rate of tax rather than seeking ever more aggressive ways to avoid it. There has been a problem in this debate in the past in that people have said: 'Well of course there is a difference between tax evasion, which is illegal and should be pursued by the full force of the law, and then there is tax avoidance which is perfectly legal and OK.'

"I think the problem with that is that there are some forms of tax avoidance that have become so aggressive that I think there are moral questions we have to answer about whether we want to encourage or allow that sort of behaviour."

Cameron said it was important to put moral pressure on tax avoiders because of the difficulty in changing the law fast enough to keep up with new schemes. "Some would say: 'Well just keep changing the law to make the aggressive avoidance illegal.' But with respect to many friends in the accountancy profession it is difficult to do that. So there is a legitimate debate to say very aggressive forms of avoidance are not appropriate, particularly in a country that set a low tax rate it is fair to ask people to pay."

The prime minister delivered a homily on the need to press ahead with infrastructure projects. Asked whether London's public transport system is a useful model for Mumbai, he said: "I am not sure I would hold up London as a perfect example. One of the things I'd say is if you know you've got to build your infrastructure even though you know it is going to take many years before it comes to fruition – start now.

"It is an area where you need proper planning. You can't leave these things to the market. You've got to have a proper plan for public transport."

Cameron, who took questions after a nine-hour flight from London, also offered details of his health and fitness regime.

"I try and stay a little bit fit. I try and go for a run a week, I try to play a game of tennis every week and I try not to go to bed too late. But like all these things that doesn't always work. But the most important things is to have a very good team around you. That is the most important thing – to make sure you can delegate and you can have a team you can work with and get things done for you.

"As I always say, if you are exhausted and if you are fried mentally you will be a hopeless prime minister. You have to try and keep a good equilibrium and balance and then hopefully you can make good decisions."